// 回归分析 - 初中数学综合题型（50题）
// 已从动态生成转换为静态题目，确保准确性

interface Question {
  stem: string;
  difficulty: number;
  answer: (string | number)[];
  hint1: string;
  hint2: string;
  solution: string;
}

export const 回归分析_QUESTIONS: Question[] = [
  { stem: "观察数据点(1,2), (2,4), (3,6)，判断x和y的关系类型。", difficulty: 1, answer: ["正相关"], hint1: "x增大，y也增大", hint2: "正相关关系", solution: "【解题】\n∵ x增大时，y也增大\n∴ x和y呈正相关\n\n答：正相关。" },
  { stem: "观察数据点(1,3), (2,6), (3,9)，判断x和y的关系类型。", difficulty: 1, answer: ["正相关"], hint1: "x增大，y也增大", hint2: "正相关关系", solution: "【解题】\n∵ x增大时，y也增大\n∴ x和y呈正相关\n\n答：正相关。" },
  { stem: "观察数据点(1,5), (2,10), (3,15)，判断x和y的关系类型。", difficulty: 1, answer: ["正相关"], hint1: "x增大，y也增大", hint2: "正相关关系", solution: "【解题】\n∵ x增大时，y也增大\n∴ x和y呈正相关\n\n答：正相关。" },
  { stem: "观察数据点(1,10), (2,8), (3,6)，判断x和y的关系类型。", difficulty: 1, answer: ["负相关"], hint1: "x增大，y减小", hint2: "负相关关系", solution: "【解题】\n∵ x增大时，y减小\n∴ x和y呈负相关\n\n答：负相关。" },
  { stem: "观察数据点(1,12), (2,10), (3,8)，判断x和y的关系类型。", difficulty: 1, answer: ["负相关"], hint1: "x增大，y减小", hint2: "负相关关系", solution: "【解题】\n∵ x增大时，y减小\n∴ x和y呈负相关\n\n答：负相关。" },
  { stem: "观察数据点(1,15), (2,12), (3,9)，判断x和y的关系类型。", difficulty: 1, answer: ["负相关"], hint1: "x增大，y减小", hint2: "负相关关系", solution: "【解题】\n∵ x增大时，y减小\n∴ x和y呈负相关\n\n答：负相关。" },
  { stem: "观察数据点(1,4), (2,8), (3,12)，判断x和y的关系类型。", difficulty: 1, answer: ["正相关"], hint1: "x增大，y也增大", hint2: "正相关关系", solution: "【解题】\n∵ x增大时，y也增大\n∴ x和y呈正相关\n\n答：正相关。" },
  { stem: "观察数据点(2,4), (3,6), (4,8)，判断x和y的关系类型。", difficulty: 1, answer: ["正相关"], hint1: "x增大，y也增大", hint2: "正相关关系", solution: "【解题】\n∵ x增大时，y也增大\n∴ x和y呈正相关\n\n答：正相关。" },
  { stem: "观察数据点(2,10), (3,8), (4,6)，判断x和y的关系类型。", difficulty: 1, answer: ["负相关"], hint1: "x增大，y减小", hint2: "负相关关系", solution: "【解题】\n∵ x增大时，y减小\n∴ x和y呈负相关\n\n答：负相关。" },
  { stem: "观察数据点(1,7), (2,14), (3,21)，判断x和y的关系类型。", difficulty: 1, answer: ["正相关"], hint1: "x增大，y也增大", hint2: "正相关关系", solution: "【解题】\n∵ x增大时，y也增大\n∴ x和y呈正相关\n\n答：正相关。" },
  { stem: "观察数据点(1,20), (2,18), (3,16)，判断x和y的关系类型。", difficulty: 1, answer: ["负相关"], hint1: "x增大，y减小", hint2: "负相关关系", solution: "【解题】\n∵ x增大时，y减小\n∴ x和y呈负相关\n\n答：负相关。" },
  { stem: "观察数据点(1,1), (2,2), (3,3)，判断x和y的关系类型。", difficulty: 1, answer: ["正相关"], hint1: "x增大，y也增大", hint2: "正相关关系", solution: "【解题】\n∵ x增大时，y也增大\n∴ x和y呈正相关\n\n答：正相关。" },
  { stem: "观察数据点(1,9), (2,7), (3,5)，判断x和y的关系类型。", difficulty: 1, answer: ["负相关"], hint1: "x增大，y减小", hint2: "负相关关系", solution: "【解题】\n∵ x增大时，y减小\n∴ x和y呈负相关\n\n答：负相关。" },
  { stem: "观察数据点(2,6), (3,9), (4,12)，判断x和y的关系类型。", difficulty: 1, answer: ["正相关"], hint1: "x增大，y也增大", hint2: "正相关关系", solution: "【解题】\n∵ x增大时，y也增大\n∴ x和y呈正相关\n\n答：正相关。" },
  { stem: "观察数据点(2,12), (3,10), (4,8)，判断x和y的关系类型。", difficulty: 1, answer: ["负相关"], hint1: "x增大，y减小", hint2: "负相关关系", solution: "【解题】\n∵ x增大时，y减小\n∴ x和y呈负相关\n\n答：负相关。" },
  { stem: "已知回归直线方程y = 2x + 1，当x = 3时，预测y的值。", difficulty: 2, answer: [7], hint1: "代入x = 3", hint2: "y = 2×3 + 1", solution: "【解题】\ny = 2×3 + 1 = 7\n\n答：y = 7。" },
  { stem: "已知回归直线方程y = 3x + 2，当x = 4时，预测y的值。", difficulty: 2, answer: [14], hint1: "代入x = 4", hint2: "y = 3×4 + 2", solution: "【解题】\ny = 3×4 + 2 = 14\n\n答：y = 14。" },
  { stem: "已知回归直线方程y = 4x + 3，当x = 2时，预测y的值。", difficulty: 2, answer: [11], hint1: "代入x = 2", hint2: "y = 4×2 + 3", solution: "【解题】\ny = 4×2 + 3 = 11\n\n答：y = 11。" },
  { stem: "已知回归直线方程y = 5x + 1，当x = 3时，预测y的值。", difficulty: 2, answer: [16], hint1: "代入x = 3", hint2: "y = 5×3 + 1", solution: "【解题】\ny = 5×3 + 1 = 16\n\n答：y = 16。" },
  { stem: "已知回归直线方程y = 2x - 1，当x = 5时，预测y的值。", difficulty: 2, answer: [9], hint1: "代入x = 5", hint2: "y = 2×5 - 1", solution: "【解题】\ny = 2×5 - 1 = 9\n\n答：y = 9。" },
  { stem: "已知回归直线方程y = 3x - 2，当x = 4时，预测y的值。", difficulty: 2, answer: [10], hint1: "代入x = 4", hint2: "y = 3×4 - 2", solution: "【解题】\ny = 3×4 - 2 = 10\n\n答：y = 10。" },
  { stem: "已知回归直线方程y = 4x - 3，当x = 3时，预测y的值。", difficulty: 2, answer: [9], hint1: "代入x = 3", hint2: "y = 4×3 - 3", solution: "【解题】\ny = 4×3 - 3 = 9\n\n答：y = 9。" },
  { stem: "已知回归直线方程y = 5x - 4，当x = 2时，预测y的值。", difficulty: 2, answer: [6], hint1: "代入x = 2", hint2: "y = 5×2 - 4", solution: "【解题】\ny = 5×2 - 4 = 6\n\n答：y = 6。" },
  { stem: "已知回归直线方程y = 6x + 1，当x = 2时，预测y的值。", difficulty: 2, answer: [13], hint1: "代入x = 2", hint2: "y = 6×2 + 1", solution: "【解题】\ny = 6×2 + 1 = 13\n\n答：y = 13。" },
  { stem: "已知回归直线方程y = 7x + 2，当x = 1时，预测y的值。", difficulty: 2, answer: [9], hint1: "代入x = 1", hint2: "y = 7×1 + 2", solution: "【解题】\ny = 7×1 + 2 = 9\n\n答：y = 9。" },
  { stem: "已知回归直线方程y = 8x + 3，当x = 1时，预测y的值。", difficulty: 2, answer: [11], hint1: "代入x = 1", hint2: "y = 8×1 + 3", solution: "【解题】\ny = 8×1 + 3 = 11\n\n答：y = 11。" },
  { stem: "已知回归直线方程y = 2x + 5，当x = 4时，预测y的值。", difficulty: 2, answer: [13], hint1: "代入x = 4", hint2: "y = 2×4 + 5", solution: "【解题】\ny = 2×4 + 5 = 13\n\n答：y = 13。" },
  { stem: "已知回归直线方程y = 3x + 4，当x = 3时，预测y的值。", difficulty: 2, answer: [13], hint1: "代入x = 3", hint2: "y = 3×3 + 4", solution: "【解题】\ny = 3×3 + 4 = 13\n\n答：y = 13。" },
  { stem: "已知回归直线方程y = 4x + 2，当x = 2时，预测y的值。", difficulty: 2, answer: [10], hint1: "代入x = 2", hint2: "y = 4×2 + 2", solution: "【解题】\ny = 4×2 + 2 = 10\n\n答：y = 10。" },
  { stem: "已知回归直线方程y = 5x + 3，当x = 2时，预测y的值。", difficulty: 2, answer: [13], hint1: "代入x = 2", hint2: "y = 5×2 + 3", solution: "【解题】\ny = 5×2 + 3 = 13\n\n答：y = 13。" },
  { stem: "已知回归直线方程y = 6x - 1，当x = 2时，预测y的值。", difficulty: 2, answer: [11], hint1: "代入x = 2", hint2: "y = 6×2 - 1", solution: "【解题】\ny = 6×2 - 1 = 11\n\n答：y = 11。" },
  { stem: "已知回归直线方程y = 7x - 2，当x = 2时，预测y的值。", difficulty: 2, answer: [12], hint1: "代入x = 2", hint2: "y = 7×2 - 2", solution: "【解题】\ny = 7×2 - 2 = 12\n\n答：y = 12。" },
  { stem: "已知回归直线方程y = 8x - 3，当x = 2时，预测y的值。", difficulty: 2, answer: [13], hint1: "代入x = 2", hint2: "y = 8×2 - 3", solution: "【解题】\ny = 8×2 - 3 = 13\n\n答：y = 13。" },
  { stem: "已知回归直线方程y = 9x - 4，当x = 2时，预测y的值。", difficulty: 2, answer: [14], hint1: "代入x = 2", hint2: "y = 9×2 - 4", solution: "【解题】\ny = 9×2 - 4 = 14\n\n答：y = 14。" },
  { stem: "已知回归直线方程y = 10x - 5，当x = 2时，预测y的值。", difficulty: 2, answer: [15], hint1: "代入x = 2", hint2: "y = 10×2 - 5", solution: "【解题】\ny = 10×2 - 5 = 15\n\n答：y = 15。" },
  { stem: "某研究发现两个变量的相关系数r = 0.2，判断相关性强弱。", difficulty: 3, answer: ["弱相关"], hint1: "|r|越接近1，相关性越强", hint2: "|r|越接近0，相关性越弱", solution: "【解题】\n|r| = 0.2\n∵ |r| < 0.6\n∴ 弱相关\n\n答：弱相关。" },
  { stem: "某研究发现两个变量的相关系数r = 0.4，判断相关性强弱。", difficulty: 3, answer: ["弱相关"], hint1: "|r|越接近1，相关性越强", hint2: "|r|越接近0，相关性越弱", solution: "【解题】\n|r| = 0.4\n∵ |r| < 0.6\n∴ 弱相关\n\n答：弱相关。" },
  { stem: "某研究发现两个变量的相关系数r = 0.6，判断相关性强弱。", difficulty: 3, answer: ["中等相关"], hint1: "|r|越接近1，相关性越强", hint2: "|r|越接近0，相关性越弱", solution: "【解题】\n|r| = 0.6\n∵ |r| = 0.6\n∴ 中等相关\n\n答：中等相关。" },
  { stem: "某研究发现两个变量的相关系数r = 0.8，判断相关性强弱。", difficulty: 3, answer: ["强相关"], hint1: "|r|越接近1，相关性越强", hint2: "|r|越接近0，相关性越弱", solution: "【解题】\n|r| = 0.8\n∵ |r| > 0.6\n∴ 强相关\n\n答：强相关。" },
  { stem: "某研究发现两个变量的相关系数r = 0.9，判断相关性强弱。", difficulty: 3, answer: ["强相关"], hint1: "|r|越接近1，相关性越强", hint2: "|r|越接近0，相关性越弱", solution: "【解题】\n|r| = 0.9\n∵ |r| > 0.6\n∴ 强相关\n\n答：强相关。" },
  { stem: "某研究发现两个变量的相关系数r = -0.7，判断相关性强弱。", difficulty: 3, answer: ["强相关"], hint1: "|r|越接近1，相关性越强", hint2: "|r|越接近0，相关性越弱", solution: "【解题】\n|r| = 0.7\n∵ |r| > 0.6\n∴ 强相关\n\n答：强相关。" },
  { stem: "某研究发现两个变量的相关系数r = -0.5，判断相关性强弱。", difficulty: 3, answer: ["弱相关"], hint1: "|r|越接近1，相关性越强", hint2: "|r|越接近0，相关性越弱", solution: "【解题】\n|r| = 0.5\n∵ |r| < 0.6\n∴ 弱相关\n\n答：弱相关。" },
  { stem: "某研究发现两个变量的相关系数r = -0.85，判断相关性强弱。", difficulty: 3, answer: ["强相关"], hint1: "|r|越接近1，相关性越强", hint2: "|r|越接近0，相关性越弱", solution: "【解题】\n|r| = 0.85\n∵ |r| > 0.6\n∴ 强相关\n\n答：强相关。" },
  { stem: "某研究发现两个变量的相关系数r = 0.95，判断相关性强弱。", difficulty: 3, answer: ["强相关"], hint1: "|r|越接近1，相关性越强", hint2: "|r|越接近0，相关性越弱", solution: "【解题】\n|r| = 0.95\n∵ |r| > 0.6\n∴ 强相关\n\n答：强相关。" },
  { stem: "某研究发现两个变量的相关系数r = 0.3，判断相关性强弱。", difficulty: 3, answer: ["弱相关"], hint1: "|r|越接近1，相关性越强", hint2: "|r|越接近0，相关性越弱", solution: "【解题】\n|r| = 0.3\n∵ |r| < 0.6\n∴ 弱相关\n\n答：弱相关。" },
  { stem: "已知数据点(1,3), (2,5), (3,7), (4,9)，求最小二乘法回归直线方程y = bx + a。", difficulty: 4, answer: ["y=2x+1"], hint1: "b = Σ(xᵢ-x̄)(yᵢ-ȳ)/Σ(xᵢ-x̄)²", hint2: "a = ȳ - bx̄", solution: "【解题】\nx̄ = 2.5，ȳ = 6\nb = 20/5 = 2\na = 6 - 2×2.5 = 1\ny = 2x + 1\n\n答：y = 2x + 1。" },
  { stem: "已知数据点(1,2), (2,4), (3,6), (4,8)，求最小二乘法回归直线方程y = bx + a。", difficulty: 4, answer: ["y=2x"], hint1: "b = Σ(xᵢ-x̄)(yᵢ-ȳ)/Σ(xᵢ-x̄)²", hint2: "a = ȳ - bx̄", solution: "【解题】\nx̄ = 2.5，ȳ = 5\nb = 20/5 = 2\na = 5 - 2×2.5 = 0\ny = 2x\n\n答：y = 2x。" },
  { stem: "已知数据点(1,4), (2,6), (3,8), (4,10)，求最小二乘法回归直线方程y = bx + a。", difficulty: 4, answer: ["y=2x+2"], hint1: "b = Σ(xᵢ-x̄)(yᵢ-ȳ)/Σ(xᵢ-x̄)²", hint2: "a = ȳ - bx̄", solution: "【解题】\nx̄ = 2.5，ȳ = 7\nb = 20/5 = 2\na = 7 - 2×2.5 = 2\ny = 2x + 2\n\n答：y = 2x + 2。" },
  { stem: "已知数据点(1,5), (2,7), (3,9), (4,11)，求最小二乘法回归直线方程y = bx + a。", difficulty: 4, answer: ["y=2x+3"], hint1: "b = Σ(xᵢ-x̄)(yᵢ-ȳ)/Σ(xᵢ-x̄)²", hint2: "a = ȳ - bx̄", solution: "【解题】\nx̄ = 2.5，ȳ = 8\nb = 20/5 = 2\na = 8 - 2×2.5 = 3\ny = 2x + 3\n\n答：y = 2x + 3。" },
  { stem: "已知数据点(1,1), (2,3), (3,5), (4,7)，求最小二乘法回归直线方程y = bx + a。", difficulty: 4, answer: ["y=2x-1"], hint1: "b = Σ(xᵢ-x̄)(yᵢ-ȳ)/Σ(xᵢ-x̄)²", hint2: "a = ȳ - bx̄", solution: "【解题】\nx̄ = 2.5，ȳ = 4\nb = 20/5 = 2\na = 4 - 2×2.5 = -1\ny = 2x - 1\n\n答：y = 2x - 1。" }
];

export default 回归分析_QUESTIONS;

